That the credit for the theorem belongs to Cantor is not under question. This is acknolwedged in the article:
>The revelation about Cantor’s result doesn’t undermine his legacy. He was still the first person to prove that there are more real numbers than whole ones, which is what ultimately opened up infinity to study.
What he is alleged to have plagiarised are the proofs, or at least one of the proofs. The original article by Goos [0] contains a lot more details about this, including a partial transcription of the letter by Dedekind that Cantor is accused of plagiarism. The story is complex.
1. Cantor's paper has two theorems: the countability of algebraic numbers and the uncountability of reals.
2. The proof of the former appears in Dedekind's letter, and Cantor acknowledges this in his response to the letter. Dedekind mentions in his letter that he only thought about proving this because of Cantor's prompt and only wrote it with the hope of helping Cantor. Dedekind felt that the proof by Cantor is "word for word" his, although it is quite the case. It is essentially the same proof though.
Cantor also felt that Dedekind's proof that the set of algebraic numbers is countable is essentially the same as his own proof of the countability of tuples. It remains that he didn't think of adapting that proof himself, and that Dedekind was the first to prove the theorem is not under question.
3. Dedekind was not the first to prove the uncountability of real numbers. However, he gave a number of ideas to Cantor in that same letter. Namely, he suggested proving the uncountability of the interval (0,1), and it seems that gave a pointer towards how to build the diagonalisation argument, although how this statement was useful to Cantor (page 76 of Goos' paper) escapes me.
EDIT: it's not a pointer to the diagonalisation argument, it is an argument why proving the theorem on (0,1) is enough.
4. Cantor proved the uncountability of reals shortly afterwards, and shared his proof with Dedekind. Dedekind simplified the proof in his reply, and Cantor seems to have come up with a similar simplification on his own. None of these letters are analysed in Goos' article.
5. Cantor published the two theorems; the first proof is essentially the same as Dedekin's, and the second proof is possibly the one Dedekind's simplified version of Cantor's. Dedekind is not acknowledged at all in that paper, due to academic politics.
Goos' paper is very detailed and quite readable. I recommend it. The site is pretty annoying and you can't download the article without creating an account, but you can read the article online.
Even if the most important theorem of the two is unquestionably creditable to Cantor, the first one should likewise unquestionably be credited to Dedekind, at least partially. This is where the accusation of plagiarism stems from.
Beyond the question on plagiarism, there is no question that Cantor and Dedekind worked together on this. The lack of acknowledgement by Cantor is certainly quite unfortunate.
This approach is just fine for the industry: delegate the problem to the lowest, shadiest bidder. After all, privacy breaches aren't their problem. If governments want an ID system they should provide one.
We have gone from the industry clamouring that what's being done now is not possible and spending millions of lobbying money against it, to such laws spreading like wildfire.
The next step is the (inevitable) mess up because implementations won't be foolproof, followed by yet more millions of lobbying money being spent to amplify the effect of these mess ups.
Eventually we will come to a new normal. It will take time. But the hope is that the cat is out of the bag and we don't come back to a model that we know hurts children and pretend it's just how it is.
It depends how you define "good writing", which is too often associated with "proper language", and by extension with proper breeding. It is a class marker.
People have a distinct voice when they write, including (perhaps even especially) those without formal training in writing. That this voice is grating to the eyes of a well educated reader is a feature that says as much about the reader as it does about the writer.
Funnily enough, professional writers have long recognised this, as is shown by the never-ending list of authors who tried to capture certain linguistic styles in their work, particularly in American literature.
There are situations where you may want this class marker to be erased, because being associated with a certain social class can have negative impact on your social prospects. But it remains that something is being lost in the process, and that something is the personality and identity of the writer.
The comments suggest to recuse the judges from countries involved, or to remove the lowest or highest scores for each contestant.
If you remove the scores given by the judges from France and the US, the French pair wins. If you remove the lowest and highest score for each contestant, the French pair wins. If you do both of those things the French pair wins.
The individual judges scores can be found here [0].
This really comes across as a smear campaign by sore losers.
Do you have advice on how to use those calculators with modern tooling? For example I remember there were cross-compilers for the hp48 [0], do you use any of that (and how do you transfer data to/from the calculators)?
No, I do not get that deep. I used to exchange data on the Ti-92 plus and the Classpad. Connecting those devices is either rather outdated (serial port with USB converter) and/or comes with vendor subscriptions, which I am not willing to pay.
> Can't they figure out what books to get without being told?
Probably not? People are not "being told" what to read, they are given some opinionated advice which they can then decide to follow or not.
According to Wikipedia, 275,000 books are published each year in the US alone [0]. Most people (even excluding the many that don't read) will read well under 0.01% of that. Deciding which books to read without taking advice from someone more informed would not be optimal.
Sometimes it makes a lot more sense to rely of expert advice than to just make all decisions on your own.
> The very fact people think they need to read (fiction) books released this year more than ones released before is baffling.
Do they really?
I was comparing rates of production vs consumption. It doesn't follow that what is being consumed on a given year is this year's production.
My guess is that most of the books written are read by hardly anyone. A few authors have a faithful following that will read their books as soon as it's out (which isn't too baffling). Reviewers and critics may indeed be more likely to review new books, which might impact people's decisions (again, not necessarily baffling). Book shops also put new books forward, but all those books tend to be the ones by trendy authors.
Other than the few fashionable books that come out each year you'll find reviewers like the one described in the article who don't seem to focus on new books (e.g. they talk about Dostoïevski), so it is not obvious that people feel that compelled to read new books.
> the backlog of books spread across millennia, not a century.
How much I agree with this! Plus, time does such a great job at filtering out the good from the bad (or the exceptional from the mundane). That's where lists of books entering the public domain, like this one [0], are important. Or the reviews [1].
Ultimately, the fact that there is more available to read than is possible even to the most voracious of readers means that most people will rely on guidance on what to read.
This quote explains why the author thinks that it is a problem :
> with string theorists now virtually unemployable unless they can figure out how to rebrand as machine learning experts.
Their issue is (seemingly) not with the paper, but with the claim that these headlines feed a hype that attribute to string theory capabilities it doesn't have.
To be clear this is OP's argument, not mine. I am not sure I buy it, except perhaps for the fact that every other academic is expected to rebrand as an ML expert nowadays. It has more to do with ML hype than with string theory hype.
The professor whose student worked on this problem is a network theorist. He's never done string theory and has no need to "rebrand as machine learning expert". So yeah I don't buy it either.
A limitation of written exams is in distance education, which simply was hardly a thing for the hundreds of years exams were used. Just like WFH is a new practice employers have to learn to deal with, study from home (SFH) is a phenomenon that is going to affect education.
The objections to SFH exist and are strikingly similar to objections to WFH, but the economics are different. Some universities already see value in offering that option, and they (of course) leave it to the faculty to deal with the consequences.
Distance education is a tiny percentage of higher education though. Online classes at a local university are more common, but you can still bring the students in for proctored exams.
Even for distance education though, proctored testing centers have been around longer than the internet.
> Distance education is a tiny percentage of higher education though.
It is about a third of the students I teach, which amounts to several hundreds per term. It may be niche, but it is not insignificant, and definitely a problem for some of us.
> Even for distance education though, proctored testing centers have been around longer than the internet.
I don't know how much experience you have with those. Mine is extensive enough that I have a personal opinion that they are not scalable (which is the focus of the comment I was replying to). If you have hundreds of students disseminated around the world, organising a proctored exam is a logistical challenge.
It is not a problem at many universities yet, because they haven't jumped on the bandwagon. However domestic markets are becoming saturated, visas are harder to get for international students, and there is a demand for online education. I would be surprised that it doesn't develop more in the near future.
I agree that proctoring across hundreds of locations globally could be a challenge.
I think the end result though is that schools either limit their students to a smaller number of locations where they can have proctored exams, or they don’t and they effectively lose their credentialing value.
Being obnoxious works well. Obnoxious people get elected to power. Obnoxious companies (and CEOs) generate hype that increases stock prices. Obnoxious youtubers call themselves influencers and make a good living out of it.
Or more charitably it is difficult to be successful without annoying many people.
* Doing flashy work, whatever that means in a given situation
What I have seen lead to failure or, at best, being undervalued and ignored:
* Caring about teammates and your future self
* Caring about the end user and the business itself, when it conflicts with something sales, marketing, or a PM want
* Creating resilient, well-engineered systems
It's the same problem as anywhere else. Well-crafted systems are invisible and taken for granted. Saving the day by putting out a fire is applauded, even when you're the one who laid out the kindling and matches. Managers at all levels care about their own ego more than the company, product, or team.
Maybe I just spent too much time with ex-Microsoft hacks.
Early on in my career I couldn't understand why it was always the worst and most incompetent people who got promoted.
Then I realized that it's not their incompetence that gets them promoted per se, it's that if they're employed while being utterly useless and incompetent they have SOMETHING else going on that keeps them employed.
And it's that something else (whether that is politics, brown nosing, nepotism, bullying) that also gets them promoted.
No, the first one thrives because they know how to play politics, the second one fails because they don't know how to play politics.
You described word for word the archetypical engineer, competent technically, incompetent politically. A liability to his team and superiors in a cut-throat corporate environment. That's why they fail, they can't be trusted to not screw their team over to do the right thing.
There is also the type of person, who just wants to do a good job and has passion for what they do well, but does not want to engage in silly political games. Just saying, it doesn't have to be incompetence at that.
During the rise of the Third Reich, a German named Dietrich Bonhoeffer rejected the path of comfortable ignorance and valiantly chose instead to stand against the banality of evil in his land. May his words haunt the collective soul of our country:
“Silence in the face of evil is itself evil: God will not hold us guiltless. Not to speak is to speak. Not to act is to act.”
If your definition of success includes - nay, depends on - arrogance, overconfidence, and style over substance, then it's fair to say that your definition of success differs greatly from many societies' norm.
Sure, capitalist, hyper-individualistic societies might say the most toxic, selfish companies are the most successful.
But in huge swathes of the world - I'm inclined to say most of the world - success is defined by quality, respect, the test of time, and how well one achieves one's stated objectives.
Even in UK, which is not exactly a socialist utopia, a business or company that is self-sustaining and well -regarded counts as way more successful than, say, Elon Musk or Dyson (since they sold out).
Your definition of success is like defining beauty as 'women with full lips and unlined' and wondering why so many of the most beautiful people you see have had surgery. And pushing for other definitions of beauty won't help, either. Most people define beauty as a spectrum or confluence of various factors which only tangentially relate to the 2 most obvious, currently fashionable factors like lips and wrinkles.
Or, more succinctly: if you define success as financial gain, you don't value moral factors. So of course your most esteemed companies won't either.
There was some company a while back, I forget what they were called, but their claim to fame was a much higher click through rate on modal popups due to them “guilting” people with dynamic messages like “No, I don’t want to save up to 50%” or “I would rather let children starve than sign up for this newsletter”.
One, I can’t believe this worked. Two, some website owners were convinced that being patronizing towards visitors was worth the extra clicks.
Someone made a funny video about this approach with a guy at Petsmart and you hear the lady say, "Ok, just follow the prompts." and gets worse/funnier from there:
Quite true. Sundar Pichai got his start on the path to fame at Google by getting the Google Toolbar install injected into things like the Adobe Acrobat and Adobe Flash installers. Look at him now.
Oh man I totally forgot about that Toolbar scourge back in the day day! These trash piles were all over and everyone’s mom that I knew had like 3 or 4.
Every year, the post-Thanksgiving ritual of deleting all of them from a relative’s PC, at their request because “it’s running slow”, knowing darn well they’d re-install them within the week.
Well, "blame the parents" is as hypocritical as "think of the children". It just displaces the responsibility of excluding kids from society from the community to the parents.
Creating a safe society for everyone is one of the roles of the state/government. That is why they are granted a monopoly on violence. As you rightly say, children are members of the society and therefore they are included in that responsibility.
The Australian government should be rightly criticized for passing a law that makes being online less safe for adults. However, that doesn't mean we should dismiss the alleged aim of the law, protecting children from harmful online content. It is a real problem that deserves serious attention.
I don’t think we should pass laws just because there was allegedly a nice thought behind him. More reasonable protections have been in discussion for long before this entered the picture. That aside, you probably missed this, but the exact same government passed a law to convict children with adult sentences in the same week as this. You probably also missed that this same government which pledged to pass ready-to-go privacy laws at the start of its previous term has taken that off the table. There were plenty of other options that were already being deliberated to deal with your concerns, but this government is the one that has “dismissed” them, not critics of this reactionary theatre.
>The revelation about Cantor’s result doesn’t undermine his legacy. He was still the first person to prove that there are more real numbers than whole ones, which is what ultimately opened up infinity to study.
What he is alleged to have plagiarised are the proofs, or at least one of the proofs. The original article by Goos [0] contains a lot more details about this, including a partial transcription of the letter by Dedekind that Cantor is accused of plagiarism. The story is complex.
1. Cantor's paper has two theorems: the countability of algebraic numbers and the uncountability of reals.
2. The proof of the former appears in Dedekind's letter, and Cantor acknowledges this in his response to the letter. Dedekind mentions in his letter that he only thought about proving this because of Cantor's prompt and only wrote it with the hope of helping Cantor. Dedekind felt that the proof by Cantor is "word for word" his, although it is quite the case. It is essentially the same proof though.
Cantor also felt that Dedekind's proof that the set of algebraic numbers is countable is essentially the same as his own proof of the countability of tuples. It remains that he didn't think of adapting that proof himself, and that Dedekind was the first to prove the theorem is not under question.
3. Dedekind was not the first to prove the uncountability of real numbers. However, he gave a number of ideas to Cantor in that same letter. Namely, he suggested proving the uncountability of the interval (0,1), and it seems that gave a pointer towards how to build the diagonalisation argument, although how this statement was useful to Cantor (page 76 of Goos' paper) escapes me.
EDIT: it's not a pointer to the diagonalisation argument, it is an argument why proving the theorem on (0,1) is enough.
4. Cantor proved the uncountability of reals shortly afterwards, and shared his proof with Dedekind. Dedekind simplified the proof in his reply, and Cantor seems to have come up with a similar simplification on his own. None of these letters are analysed in Goos' article.
5. Cantor published the two theorems; the first proof is essentially the same as Dedekin's, and the second proof is possibly the one Dedekind's simplified version of Cantor's. Dedekind is not acknowledged at all in that paper, due to academic politics.
Goos' paper is very detailed and quite readable. I recommend it. The site is pretty annoying and you can't download the article without creating an account, but you can read the article online.
Even if the most important theorem of the two is unquestionably creditable to Cantor, the first one should likewise unquestionably be credited to Dedekind, at least partially. This is where the accusation of plagiarism stems from. Beyond the question on plagiarism, there is no question that Cantor and Dedekind worked together on this. The lack of acknowledgement by Cantor is certainly quite unfortunate.
[0] https://www.scribd.com/document/977967855/Phlogiston-33#page...
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